Has anyone travelled recently on a Thomson flight and taken their child in a car seat, and if so, how was the experience?

We are booked to go Greece this summer and at the moment we have only booked seats for ourselves with our son going as a lap chile (he'll be 17 months). After thinking about it, I have decided to book a seat for him in an attempt to make it more enjoyable for all concerned (plus a lot safer for him). It will mean buying a new car seat as the one in our car is too big, and this is where my confusion starts.

Thomson state that it must be less that 16in/40cm, however all the ones I've looked at seem to state the smallest dimension as 45cm. I don't want to go to all the trouble of buying one, carting it onto the plane, and then getting told by a FA who isn't completley up to date that it needs to go into the hold.

Their website states that it must be approved for air travel (quite a few do specifically mention FAA approved) but it is the dimensions that get me. A seat may be FAA approved (does that mean it is also ok for a UK flight?) for travel but that doesn't necessary mean it will fit into the "cosy" seats that Thomson use.

Any help or advice would be greatly appreciated.